Synthesis of Output-Feedback Controllers for Mixed Traffic Systems in Presence of Disturbances and Uncertainties

In this paper, we study mixed traffic systems that move along a single-lane ring-road or open-road. The traffic flow forms a platoon, which includes a number of heterogeneous human-driven vehicles (HDVs) together with only one connected and automated vehicle (CAV) that receives information from a subset of neighbors. The dynamics of HDVs are assumed to follow a general continuous-time nonlinear car-following model, which is a function of their velocity, spacing, and the relative velocity. The acceleration of the single CAV is also directly controlled by a dynamical output-feedback controller. The ultimate goal of this work is to present a robust control strategy that can smoothen the traffic flow in the presence of undesired disturbances (e.g. abrupt deceleration) and parametric uncertainties. A prerequisite for synthesizing a dynamical output controller is the stabilizability and detectability of the underlying system. Accordingly, a theoretical analysis is presented first to prove the stabilizability and detectability of the mixed traffic flow system. Then, two $H_\infty $ control strategies, with and without considering uncertainties in the system dynamics, are designed. The efficiency of the two control methods is subsequently illustrated through numerical simulations, and various experimental results are presented to demonstrate the effectiveness of the proposed controller to mitigate disturbance amplification and achieve platoon stability.